Thursday 25 August 2005

G1
1300-1500 hours

387
Discrete Crossover Analysis (DCA)
Bosch, Wolfgang¹
1 DGFI, Munich, Germany
Author email: bosch@dgfi.badw.de
Analysis of crossover differences, performed between redundant observations at intersecting profiles, is a powerful tool, to estimate systematic errors and to cross-calibrate different observation systems. A new technique for a discrete crossover analysis (DCA) has been developed, minimizing by least squares the crossover differences without inventing a functional error model. Instead, the error components xi and xk for the two intersecting profiles are taken themselves as solve-for parameters. To ensure a certain degree of smoothness consecutive error components xi and xi+1 are minimized in parallel to the residuals of the crossover differences. Prior knowledge about the errors in terms of the auto-covariance function can be taken into account and a relative weighting between crossover and the consecutive differences is applied to balance smoothness and crossover residuals. In general, the DCA leads to a huge, but sparse normal equation matrix, composed of a tridiagonal part and a sparse matrix structure. This system of equations can be solved by an iterative conjugate gradient projection (CGP) algorithm. The standard CGP algorithm is modified such that the tridiagonal part and the sparse structure are treated seperately with the advantage that the iterative solution becomes rather fast and has very low storage requirements. The DCA has a rank defect of exactly one. To make the system regular a single error component is fixed or a linear combination of error components are introduced as constraint.

Return to Oral Presentations